Detailed Description

When data is transferred during coarsening, it is not trivial to decide how to handle data of child cells which will be coarsened. Or in other words, which data should be stored in the corresponding parent cell.

Return the sum over all processors of the value t. This function is collective over all processors given in the communicator. If deal.II is not configured for use of MPI, this function simply returns the value of t. This function corresponds to the MPI_Allreduce function, i.e. all processors receive the result of this operation.

Note

Sometimes, not all processors need a result and in that case one would call the MPI_Reduce function instead of the MPI_Allreduce function. The latter is at most twice as expensive, so if you are concerned about performance, it may be worthwhile investigating whether your algorithm indeed needs the result everywhere.

Note: This differs from what is typically known as the mean of a function by a factor of \(\frac{1}{|\Omega|}\). To compute the mean you can also use compute_mean_value(). Finally, pay attention to the sign: if \(\hat{f}=0\), this will compute the negative of the mean of \(f\).